On-line item generation is becoming increasingly feasible for many cognitive tests. Item generation seemingly conflicts with the well established principle of measuring persons from items with known psychometric properties. This paper examines psychometric principles and models required for measurement from on-line item generation. Three psychometric issues are elaborated for item generation. First, design principles to generate items are considered. A cognitive design system approach is elaborated and then illustrated with an application to a test of abstract reasoning. Second, psychometric models for calibrating generating principles, rather than specific items, are required. Existing item response theory (IRT) models are reviewed and a new IRT model that includes the impact on item discrimination, as well as difficulty, is developed. Third, the impact of item parameter uncertainty on person estimates is considered. Results from both fixed content and adaptive testing are presented.

In this paper, the constrained maximum likelihood estimation of a two-level covariance structure model with unbalanced designs is considered. The two-level model is reformulated as a single-level model by treating the group level latent random vectors as hypothetical missing-data. Then, the popular EM algorithm is extended to obtain the constrained maximum likelihood estimates. For general nonlinear constraints, the multiplier method is used at the M-step to find the constrained minimum of the conditional expectation. An accelerated EM gradient procedure is derived to handle linear constraints. The empirical performance of the proposed EM type algorithms is illustrated by some artifical and real examples.

The partial derivative matrices of the class of orthomax-rotated factor loadings with respect to the unrotated maximum likelihood factor loadings are derived. The reported results are useful for obtaining standard errors of the orthomax-rotated factor loadings, with or without row normalization (standardization) of the initial factor loading matrix for rotation. Using a numerical example, we verify our analytic formulas by comparing the obtained standard error estimates with that from some existing methods. Some advantages of the current approach are discussed.

The estimation of model parameters in structural equation models with polytomous variables can be handled by several computationally efficient procedures. However, sensitivity or influence analysis of the model is not well studied. We demonstrate that the existing influence analysis methods for contingency tables or for normal theory structural equation models cannot be applied directly to structural equation models with polytomous variables; and we develop appropriate procedures based on the local influence approach of Cook (1986). The proposed procedures are computationally efficient, the necessary bits of the proposed diagnostic measures are readily available following an usual fit of the model. We consider the influence of an individual cell frequency with respect to three cases: when all parameters in an unstructured model are of interest, when the unstructured polychoric correlations are of interest, and when the structural parameters are of interest. We also consider the sensitivity of the parameters estimates. Two examples based on real data are presented for illustration.

Models and parameters of finite mixtures of multivariate normal densities conditional on regressor variables are specified and estimated. We consider mixtures of multivariate normals where the expected value for each component depends on possibly nonnormal regressor variables. The expected values and covariance matrices of the mixture components are parameterized using conditional mean- and covariance-structures. We discuss the construction of the likelihood function, estimation of the mixture model with regressors using three different EM algorithms, estimation of the asymptotic covariance matrix of parameters and testing for the number of mixture components. In addition to simulation studies, data on food preferences are analyzed.

Factor scores are naturally predicted by means of their conditional expectation given the indicators y. Under normality this expectation is linear in y but in general it is an unknown function of y. It is discussed that under nonnormality factor scores can be more precisely predicted by a quadratic function of y.